X^2=16^X Find the value of x

JBxOnline asked Mar 3, 2022

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24 votes

X^2=16^X
Find the value of x

JBxOnline asked Mar 3, 2022

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11 votes

Answer:

${x}^(2) = {16}^(x) \\ \\ {x}^(2) = 2 {}^(4x)$

introduce logarithm of base 10:

$log( {x}^(2) ) = log( {2}^(4x) ) \\ \\ 2 log(x) = 4x log(2) \\ \\ log(x) = 0.6x \\ \\ x = 4 .{10}^(x)$

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